In Ethical Intuitionism, Huemer claims that there are only three possible forms of antirealism:
(1) Noncognitivism
(2) Subjectivism
(3) Error theory
This is not true.
First, if Huemer conceives of these positions as uniform (see Gill, 2009), this would ignore the possibility of metaethical pluralism. A uniform account assigns the same meaning to all moral claims (excluding errors, idiosyncratic usage, sarcasm, and other instances of noncentral usage).
If noncognitivism is denoted with {N}, subjectivism with {S}, and error theory with {E}, this means if we looked at moral claims, we’d observe one of the following possibilities:
1. Noncognitivism
Moral claims = {N, N, N, N, N, N, N, N, N, N}
2. Subjectivism
Moral claims = {S, S, S, S, S, S, S, S, S, S}
3. Error theory
Moral claims = {E, E, E, E, E, E, E, E, E, E}
However, it is possible that the uniformity is false. In which case, we could observe something like this:
4. Pluralism
Moral claims = {N, S, E, E, N, N, S, E, S, N}
If pluralism is the correct account of moral claims, then all three traditional accounts are false.
I don’t know if Huemer endorses uniformity. If he does, and if pluralism is possible, then the claim that there are only three possible accounts is false. Historically, some prominent philosophers have presumed uniformity (See Gill, 2009 and Sinnott-Armstrong, 2009 for examples).
However, critics could object that we could just drop uniformity (if we ever assumed it all) and maintain that all moral claims still fit one of these three analyses. At best, pluralism would represent a hybrid account, a combination of two or three of the traditional analyses.
For comparison, suppose someone said that there are only three possibilities:
(i) All objects are apples
(ii) All objects are oranges
(iii) All objects are bananas
If we discovered that (i)-(iii) were false because some objects were apples, some oranges, and some bananas, this would arguably not be such a dramatic discovery. We could just drop uniformity and maintain that for any given object, there are only three possibilities for what it could be.
However, Loeb (2008) proposes another possibility. It could be that when people make moral claims, they are simultaneously committed to two or more metaethical presuppositions, even if those presuppositions conflict with one another. This would be a bit like someone saying, “square circles exist.” The properties of a square and a circle preclude one another, but this doesn't mean a person couldn’t insist that there are such things.
Just the same, it could be that ordinary moral claims are committed to similarly conflicting presuppositions. For instance, suppose that when people make moral claims they mean both to convey a propositional claim and to not convey a propositional claim. In other words, suppose moral claims were committed to both cognitivism, which we can denote with {C}, and noncognitivism, which we can denote with {~C} to highlight that it is the negation of cognitivism. This would result in a set of claims that are not false in the way error theorists propose, but that are incoherent. Loeb refers to this possibility as “incoherentism,” and it could result in an analysis like this:
5. Incoherentism
Moral claims = {C|~C, C|~C, C|~C, C|~C, C|~C}
Incoherentism would represent a distinct alternative to the three traditional analyses and pluralism. It would not be enough merely to show that incoherentism is false, or even absurd. Huemer claims that the three traditional accounts are the only possible accounts. So Huemer would have to show that incoherentism is impossible.
Even incoherentism may not be satisfying as an alternative to the traditional three accounts. A critic may point out this both C and ~C are already encompassed by Huemer’s three categories, and this really amounts to ascribing both to a given moral claim at the same time, a bit like saying that apples and oranges are mutually exclusive, so something could be an apple or an orange, but not both, while at the same time claiming that nevertheless fruit claims presume that an object can be both an apple and an orange. Such claims still limit the meaning of fruit claims to the original categories.
This brings us to a sixth and final possibility: that the answer is “none of the above.” This view is known as metaethical indeterminacy. Metaethical indeterminacy holds that there may be cases where there is no way to determine which of two or more competing analyses of moral claims is correct. Competing accounts don’t do any better a job of accounting for the meaning of moral claims. This could be because they both do an equally adequate job, or an equally inadequate job. This could be because there is simply no fact of the matter which of two accounts is correct. There is much more to say about indeterminacy, but for now I’ll illustrate the notion with an example.
Suppose we wanted to know what people mean when they make causal claims, like “Alex will drive to work tomorrow.” We might be interested in whether such claims presuppose the Copenhagen or Many Worlds interpretation of quantum mechanics, since each suggests a different account of what happens during certain events. Most people who make causal claims don’t presuppose any interpretation of quantum mechanics. Such distinctions are simply not relevant to such claims. People don’t have to endorse any particular account of quantum mechanics when making causal claims, so it simply doesn’t make sense to insist causal claims must presuppose a specific account of quantum mechanics.
Likewise, moral claims may not presuppose stance-dependence or stance-independence either, in which case there’d be no fact of the matter about whether e.g., “murder is wrong” best fits a realist or antirealist analysis.
If moral claims were indeterminate with respect to traditional metaethical distinctions, we’d get an analysis like this:
6. Indeterminacy
Moral claims = {?, ?, ?, ?, ?, ?, ?, ?, ?, ?}
If indeterminacy is possible, then Huemer’s claim that (1)-(3) are the only possibilities is false.
References
Gill, M. B. (2009). Indeterminacy and variability in meta-ethics. Philosophical Studies, 145(2), 215-234.
Loeb, D. (2008). Moral incoherentism: How to pull a metaphysical rabbit out of a semantic hat. In W. Sinnott-Armstrong (Ed.), Moral psychology: The cognitive science of morality (Vol. 2, pp. 355-386). Cambridge, MA: MIT Press.
Sinnott-Armstrong, W. (2009). Mixed-up meta-ethics. Philosophical Issues 19(1), 235-256.



There definitely is something weird about the compulsion (?) of some philosophers to bring all anti-realist positions under the three traditional categories, even when doing so doesn’t make much sense.
In his reply to Loeb’s incoherentism paper, Sayre-McCord acknowledges Loeb’s claim to undermine “metaethical cognitivism and noncognitivism alike, since no version of either could legitimately claim to capture what we all are doing in using moral language”. And yet he proceeds to describe the varitieties of incoherentism advanced by Loeb as falling into either "incoherentist error theory" (because we're expressing incoherent concepts and there is something erroneous about that as Loeb himself admits) or the “incoherentist non-cognitivism” (because moral terms fail to express concepts at all).
The first part is dubious at best because Loeb makes it clear his incoherentism rejects the semantic thesis of the traditional error theories, as well as the underlying uniformity assumption. Calling it a form of "error theory" may create an impression to the contrary.
No less weird is the attempt to classify some instances of semantic incoherence as falling under non-cognitivism [just because?] when speaking incoherently in this way we fail to express concepts. Sayre-McCord himself admits that “incoherentist non-cognitivism” implies that there isn’t “any interestingly systematic (albeit noncognitive) role played by moral terms”. So why lump it together with non-cognitivism?
Perhaps one could conceive of incoherentism as a combination of the more traditional positions. But it would certainly be a weird and confusing way of putting it. There just aren’t any good practical reasons for doing so.
Loeb, for instance, writes: "Alternatively, it could be that there is incoherence at a higher level, that there is so much confusion and diversity with respect to the linguistic dispositions surrounding our use of the moral vocabulary that it does not make sense to think of our moral sentences as making any particular assertions or expressing any particular attitudes." Is this type of incoherence a form of error theory? Of non-cognitivism? A “combination” of both? I don't think so.